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arXiv · 1903.06222

Dp-minimal expansions of discrete ordered abelian groups

Erik Walsberg
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Abstract

If $\mathcal{Z}$ is a dp-minimal expansion of a discrete ordered abelian group $(Z,<,+)$ and $\mathcal{Z}$ does not admit a nontrivial definable convex subgroup then $\mathcal{Z}$ is interdefinable with $(Z,<,+)$ and $(Z,<,+)$ is elementarily equivalent to $(\mathbb{Z},<,+)$.

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Erik Walsberg. 2019-03-14. Dp-minimal expansions of discrete ordered abelian groups. https://arxiv.org/abs/1903.06222

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